YES

Problem:
 active(f(f(a()))) -> mark(f(g(f(a()))))
 mark(f(X)) -> active(f(X))
 mark(a()) -> active(a())
 mark(g(X)) -> active(g(mark(X)))
 f(mark(X)) -> f(X)
 f(active(X)) -> f(X)
 g(mark(X)) -> g(X)
 g(active(X)) -> g(X)

Proof:
 DP Processor:
  DPs:
   active#(f(f(a()))) -> g#(f(a()))
   active#(f(f(a()))) -> f#(g(f(a())))
   active#(f(f(a()))) -> mark#(f(g(f(a()))))
   mark#(f(X)) -> active#(f(X))
   mark#(a()) -> active#(a())
   mark#(g(X)) -> mark#(X)
   mark#(g(X)) -> g#(mark(X))
   mark#(g(X)) -> active#(g(mark(X)))
   f#(mark(X)) -> f#(X)
   f#(active(X)) -> f#(X)
   g#(mark(X)) -> g#(X)
   g#(active(X)) -> g#(X)
  TRS:
   active(f(f(a()))) -> mark(f(g(f(a()))))
   mark(f(X)) -> active(f(X))
   mark(a()) -> active(a())
   mark(g(X)) -> active(g(mark(X)))
   f(mark(X)) -> f(X)
   f(active(X)) -> f(X)
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
  Matrix Interpretation Processor: dim=3
   
   usable rules:
    active(f(f(a()))) -> mark(f(g(f(a()))))
    mark(f(X)) -> active(f(X))
    mark(a()) -> active(a())
    mark(g(X)) -> active(g(mark(X)))
    f(mark(X)) -> f(X)
    f(active(X)) -> f(X)
    g(mark(X)) -> g(X)
    g(active(X)) -> g(X)
   interpretation:
    [mark#](x0) = [1 1 0]x0,
    
    [f#](x0) = [0 1 0]x0,
    
    [g#](x0) = [0 1 0]x0,
    
    [active#](x0) = [0 1 1]x0,
    
                 [1 1 0]     [0]
    [mark](x0) = [1 1 0]x0 + [1]
                 [0 0 1]     [0],
    
              [0 1 1]     [1]
    [g](x0) = [1 0 0]x0 + [1]
              [0 0 0]     [0],
    
                   [1 0 0]     [0]
    [active](x0) = [0 1 1]x0 + [1]
                   [0 0 1]     [0],
    
              [1 0 1]     [1]
    [f](x0) = [0 0 1]x0 + [0]
              [1 0 1]     [0],
    
          [1]
    [a] = [0]
          [0]
   orientation:
    active#(f(f(a()))) = 4 >= 0 = g#(f(a()))
    
    active#(f(f(a()))) = 4 >= 3 = f#(g(f(a())))
    
    active#(f(f(a()))) = 4 >= 3 = mark#(f(g(f(a()))))
    
    mark#(f(X)) = [1 0 2]X + [1] >= [1 0 2]X = active#(f(X))
    
    mark#(a()) = 1 >= 0 = active#(a())
    
    mark#(g(X)) = [1 1 1]X + [2] >= [1 1 0]X = mark#(X)
    
    mark#(g(X)) = [1 1 1]X + [2] >= [1 1 0]X + [1] = g#(mark(X))
    
    mark#(g(X)) = [1 1 1]X + [2] >= [1 1 0]X + [1] = active#(g(mark(X)))
    
    f#(mark(X)) = [1 1 0]X + [1] >= [0 1 0]X = f#(X)
    
    f#(active(X)) = [0 1 1]X + [1] >= [0 1 0]X = f#(X)
    
    g#(mark(X)) = [1 1 0]X + [1] >= [0 1 0]X = g#(X)
    
    g#(active(X)) = [0 1 1]X + [1] >= [0 1 0]X = g#(X)
    
                        [4]    [3]                     
    active(f(f(a()))) = [5] >= [4] = mark(f(g(f(a()))))
                        [3]    [2]                     
    
                 [1 0 2]    [1]    [1 0 1]    [1]               
    mark(f(X)) = [1 0 2]X + [2] >= [1 0 2]X + [1] = active(f(X))
                 [1 0 1]    [0]    [1 0 1]    [0]               
    
                [1]    [1]              
    mark(a()) = [2] >= [1] = active(a())
                [0]    [0]              
    
                 [1 1 1]    [2]    [1 1 1]    [2]                     
    mark(g(X)) = [1 1 1]X + [3] >= [1 1 0]X + [2] = active(g(mark(X)))
                 [0 0 0]    [0]    [0 0 0]    [0]                     
    
                 [1 1 1]    [1]    [1 0 1]    [1]       
    f(mark(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = f(X)
                 [1 1 1]    [0]    [1 0 1]    [0]       
    
                   [1 0 1]    [1]    [1 0 1]    [1]       
    f(active(X)) = [0 0 1]X + [0] >= [0 0 1]X + [0] = f(X)
                   [1 0 1]    [0]    [1 0 1]    [0]       
    
                 [1 1 1]    [2]    [0 1 1]    [1]       
    g(mark(X)) = [1 1 0]X + [1] >= [1 0 0]X + [1] = g(X)
                 [0 0 0]    [0]    [0 0 0]    [0]       
    
                   [0 1 2]    [2]    [0 1 1]    [1]       
    g(active(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = g(X)
                   [0 0 0]    [0]    [0 0 0]    [0]       
   problem:
    DPs:
     
    TRS:
     active(f(f(a()))) -> mark(f(g(f(a()))))
     mark(f(X)) -> active(f(X))
     mark(a()) -> active(a())
     mark(g(X)) -> active(g(mark(X)))
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
   Qed